Problem: The sum of two numbers is $125$, and their difference is $55$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 125}$ ${x-y = 55}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 180 $ $ x = \dfrac{180}{2} $ ${x = 90}$ Now that you know ${x = 90}$ , plug it back into $ {x+y = 125}$ to find $y$ ${(90)}{ + y = 125}$ ${y = 35}$ You can also plug ${x = 90}$ into $ {x-y = 55}$ and get the same answer for $y$ ${(90)}{ - y = 55}$ ${y = 35}$ Therefore, the larger number is $90$, and the smaller number is $35$.